The bigger problem is that the Raspberry Pico is a dual-core Cortex-M0+, which doesn't have an MMU, so it can't run Linux and especially can't handle fork(). But httpdito is basically scripting the Linux system call interface in assembly language—it needs to run on top of a filesystem, an implementation of multitasking that provides allocation of different memory to different tasks, and a TCP/IP stack. Any one of these is probably a larger amount of complexity than the 296 CPU instructions in httpdito.
The smallest TCP/IP stack I know of is Adam Dunkels's uIP. Running `sloccount .` in uip/uip cloned from https://github.com/adamdunkels/uip gives a count of 2796 lines of source code ("generated using David A. Wheeler's 'SLOCCount'."). uIP can run successfully on systems with as little as 2KiB of RAM, as long as you have somewhere else to put the code, but for most uses lwIP is a better choice; it minimally needs 10KiB or so. uIP is part of Dunkels's Contiki, which includes a fairly full-featured web server and a somewhat less-full-featured browser. I think he got both the server and the browser to run in 16KiB of RAM on a Commodore PET, but not at the same time.
(twIP http://dunkels.com/adam/twip.html is only 139 bytes of C source but doesn't support TCP or any physical-layer protocol such as Ethernet, PPP,or SLIP.)
However, Adam Dunkels has also written Miniweb http://dunkels.com/adam/miniweb/, which implements HTTP and enough of TCP and IP to support it, in 400 lines of C. It needs at least 30 bytes of RAM. Like twIP, it doesn't provide a physical layer. But that's solvable.